# How many microstates are defined to exist at absolute zero for a perfect crystal?

Jun 6, 2017

-273°C corresponds to $\text{0 K}$ on the absolute scale.

The third law of thermodynamics states that in that case, the absolute entropy becomes zero for a perfect crystal:

$S = 0$ at $T = \text{0 K}$.

Statistically, from Boltzmann's theorem, $S = {k}_{B} \ln W$

$S = 0 \implies \ln W = 0$

where $W$ is the number of microstates occupied.

Thus, $W = 1$ which means that this is the most ordered state with number of microstates = 1.

However, quantum fluctuations make it difficult that such a state becomes localised because the fluctuations occurring are non-negligible compared to the energy available.

This has an important implication - absolute zero is difficult to maintain.